The Bayesian Synthetic Control: A Probabilistic Framework for Counterfactual Estimation in the Social Sciences

Abstract

Social sciences know limited methods for counterfactual estimation, i.e. approximating how a variable of interest would have developed without a particular policy intervention. Recent frequentist work has developed for the purpose a tool known as the Synthetic Control Method (SCM). SCM continues to suffer of certain flaws, including its inability to produce a confidence interval. In this senior thesis I develop a new Bayesian statistical methodology for counterfactual estimation inspired by the synthetic control method. I use pre-intervention data to model the target society’s trajectory on underlying developments that can be inferred from data on control societies. My proposed method is less prone to overfit than synthetic controls and better able to describe estimate uncertainty. I implement the method for two previously studied research questions: German re-unification in 1990 and a California tobacco control reform in 1988. To estimate the model computationally, I use a standard MCMC sampling approach. My approach outperforms SCM in a simple test of predictive accuracy.